PCB Package Substrate In-Plane Coefficient of Thermal Expansion (CTE) Testing

The in-plane coefficient of thermal expansion (CTE) of a PCB package substrate determines how much the material expands in the X-Y plane as temperature changes, directly governing solder joint reliability, die-attach integrity, and package warpage in semiconductor devices. Professional in-plane CTE testing based on thermomechanical analysis (TMA) and dilatometry, performed in accordance with IPC-TM-650 and ASTM standards, provides accurate and traceable data for material qualification, supplier comparison, and process control. This article explains the test principles, sample requirements, testing methods, acceptance criteria, and typical applications of package substrate in-plane CTE evaluation.

Technical Overview

Package substrates act as the mechanical and electrical interface between the silicon die and the motherboard in BGA, LGA, CSP, QFN, and flip-chip packages. Throughout reflow assembly, burn-in, and field operation, these substrates undergo repeated thermal excursions, and their dimensional stability over temperature is therefore a first-order reliability parameter.

The coefficient of thermal expansion (CTE) quantifies the fractional change in length per unit change in temperature, expressed in ppm/°C. For laminated substrates, the in-plane CTE (also called X-Y or IP CTE) is of particular importance because it governs the shear strain imposed on solder joints between the die, the substrate, and the assembly board. Silicon expands at approximately 2.6 ppm/°C, while typical organic substrates expand at 10 to 17 ppm/°C in-plane; this mismatch, multiplied by temperature swing and joint distance from the neutral point, drives solder fatigue, underfill delamination, and low-k die cracking.

Because organic substrate materials are polymer-based composites, their expansion behavior changes sharply at the glass transition temperature (Tg). Below Tg the material exhibits a lower expansion rate (α1), while above Tg the rate increases significantly (α2). Reliable CTE characterization therefore requires accurate temperature control, precise displacement measurement, and correct segmentation of the test temperature range.

Testing Samples

BT and Epoxy Laminate Substrates

Bismaleimide triazine (BT) and epoxy-glass laminate cores used in lead-frame substrates, memory modules, and CSP carriers are tested as bare laminate panels or as etched substrate coupons. Typical specimens are rectangular strips cut along the warp (machine) and fill (transverse) directions to characterize CTE anisotropy introduced by glass-fiber reinforcement.

ABF Build-Up Substrates

Ajinomoto build-up film (ABF) and similar photo-dielectric incremental layers used in flip-chip substrates are evaluated for both core and build-up layer contributions. Highly silica-filled films are engineered specifically for low in-plane CTE, and testing verifies that the finished stack-up meets the target expansion budget near the die.

Flexible and Rigid-Flex Substrates

Polyimide-based flexible substrates and rigid-flex constructions used in sensors, camera modules, and wearable devices are tested in both the machine and transverse directions, often at extended low-temperature ranges to reflect automotive and consumer operating environments.

Ceramic and Hybrid Substrates

Alumina, aluminum nitride, LTCC, and HTCC ceramic substrates exhibit low and nearly linear expansion (typically 4 to 8 ppm/°C) and are tested where die-matched expansion is required for high-power or hermetic packages.

Raw Laminate, Prepreg, and Copper-Clad Panels

Laminate manufacturers and incoming quality departments test raw sheets, prepreg cured stacks, and copper-clad laminates to verify compliance with material specifications such as IPC-4101 slash sheets before substrate fabrication begins.

Testing Items

Standard in-plane CTE evaluation programs typically include the following measured parameters:

• In-plane CTE below Tg (α1) over a defined range such as 30 °C to 150 °C
• In-plane CTE above Tg (α2) over a defined range such as 180 °C to 260 °C
• Z-axis (through-thickness) CTE, α1 and α2, critical for via and plated hole reliability
• Glass transition temperature (Tg) by TMA, derived from the inflection point of the expansion curve
• CTE anisotropy ratio between warp (MD) and fill (TD) directions
• Delta expansion and total dimensional change across a simulated reflow profile

Custom temperature ranges, such as −40 °C to 288 °C for lead-free reflow simulation or low-temperature automotive profiles, can be defined to match the intended application and qualification plan.

Testing Methods

Thermomechanical Analysis (TMA)

TMA is the primary method for package substrate CTE testing. The specimen is placed on a quartz platform with a low-mass expansion probe applying a small static force, and the furnace ramps at a controlled rate (commonly 5 °C/min) under nitrogen purge. Displacement resolution of 0.1 µm or better allows accurate measurement of the micrometer-scale expansion of thin substrate strips. CTE is calculated as the slope of the dimension-versus-temperature curve, obtained by linear regression over the specified interval. TMA methods follow IPC-TM-650 Method 2.4.24 series and ASTM E831.

Push-Rod Dilatometry

Horizontal or vertical dilatometers with long specimens (typically 25 to 50 mm) provide excellent precision for low-expansion materials and ceramic substrates, and are well suited to comparative supplier studies. Dilatometry is performed per ASTM E228, and quartz-tube systems for polymer films follow ASTM D696.

Foil Strain Gauge Method

For finished substrates with complex copper patterns, high-temperature strain gauges bonded to the surface measure local expansion behavior under controlled heating, following IPC-TM-650 Method 2.4.24.1. This approach captures the effective CTE of the composite structure including copper balancing effects.

Sample Preparation and Conditioning

Specimens are cut as strips along the machine and transverse directions, typically 6 to 10 mm long for TMA or 25 to 50 mm for dilatometry, with thickness built up above approximately 0.5 mm by stacking when necessary. Edges are machined flat and parallel. Samples are baked at 105 to 125 °C to remove moisture, then conditioned at 23 ± 2 °C and 50 ± 5 % RH before testing. A first heating run is frequently used to relieve residual stress, and the second run is recorded as the reported result. A minimum of three specimens per direction is recommended.

Calibration, Data Reduction, and Reporting

Instruments are calibrated for displacement using certified reference materials such as aluminum (23.1 ppm/°C), copper (16.5 ppm/°C), borosilicate glass, and fused silica, and for temperature using indium and zinc melting-point standards. The test report presents individual and mean CTE values with regression intervals, the expansion curve with Tg identification, specimen orientation, conditioning history, and full traceability to the applied standard.

Applications

In-plane CTE data supports every stage of the package and substrate lifecycle:

• Material qualification and incoming inspection of laminates, prepregs, and build-up films against supplier datasheets and IPC-4101 requirements
• Stack-up design and material selection to balance CTE between the die, underfill, substrate, and assembly board
• Finite element warpage and thermomechanical stress modeling, including JEDEC JESD22-B112 warpage prediction
• Reliability qualification supporting temperature cycling and thermal shock testing per JESD22-A104 and related profiles
• Process engineering evaluation of lamination, curing, and post-cure effects on dimensional stability
• Failure analysis to confirm whether CTE drift or Tg shift contributed to solder fatigue, delamination, or joint opens

Typical acceptance references include in-plane α1 of 10 to 15 ppm/°C for standard BT substrates, below 10 ppm/°C for low-expansion grades, 7 to 20 ppm/°C for highly filled build-up films, 40 to 60 ppm/°C for Z-axis α1, and 150 to 300 ppm/°C for Z-axis α2, with exact limits set by the product specification.

FAQ

What is the difference between in-plane and Z-axis CTE?

In-plane CTE describes expansion along the X and Y axes of the substrate and governs solder joint strain and warpage, while Z-axis CTE describes through-thickness expansion and governs copper via, plated hole, and interconnect stress. Laminates are strongly anisotropic, so both directions should be characterized.

What specimen size and quantity are required?

TMA specimens are typically strips 6 to 10 mm long, while dilatometer specimens are 25 to 50 mm long, with thickness above approximately 0.5 mm achieved by stacking thin substrates. A minimum of three specimens in each of the warp and fill directions is recommended for statistically valid results.

What temperature range and heating rate are used?

Common programs span 30 °C to 260 °C at 5 °C/min under nitrogen, with CTE reported separately below and above Tg. Custom ranges from −40 °C to 288 °C can be selected to simulate automotive, burn-in, or lead-free reflow conditions.

Why is CTE measured both below and above Tg?

Polymer composites expand at a low rate (α1) in the glassy state below Tg and at a much higher rate (α2) in the rubbery state above Tg. Both values are needed to predict behavior across reflow peaks and high-temperature operating life, where α2 dominates laminate growth and interconnect stress.

Which test method is most suitable for my sample?

TMA is the standard choice for organic package substrates due to its small specimen requirement and direct compatibility with IPC-TM-650 methods. Dilatometry offers superior precision for ceramics and long-strip laminates, and the strain gauge method is preferred when the effective CTE of a finished, patterned substrate must be captured.

Can finished substrates with copper patterns be tested?

Yes. Copper layers and pattern density modify the effective expansion of the composite, and testing finished coupons, either by TMA on patterned strips or by the strain gauge method, provides the real CTE that determines actual package warpage and solder joint loading.